For the following multiple linear regression model y = Bo + B1x1 + B2x2 + B3x3 + B4x4 + € Derive the test statistic to test Ho : B1 = B2 B3 = B4
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?Which of the multivariate regression parameters listed below would be best interpreted as: the predicted value on the dependent variable when all of the independent variables in the model are equal to zero. a b1 X1 R2Which of the following does not need to be computed to determine a simple regression line? SSx SP "Y-hat" SSy
- In the following model, "employed" is a dummy indicating a person is employed: donation = B + B edu + Bemployed + uT Running this model will produce the same results of differential in donation between employed people and unemployed people as running two separate regressions for employed people and unemployed people. A. True B. FalseIn a laboratory experiment, data were gathered on the life span (y in months) of 33 rats, units of daily protein intake (x1), and whether or not agent x2 (a proposed life-extending agent) was added to the rats' diet (x2 = 0 if agent x2 was not added, and x2 = 1 if agent was added). From the results of the experiment, the following regression model was developed:ŷ = 36 + .8x1 − 1.7x2Also provided are SSR = 60 and SST = 180.The test statistic for testing the significance of the model is _____. a. 5.00 b. .50 c. .25 d. .33The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old female individual is _____.
- The following table gives the marks obtained by 10 students in POLI 344 (X) together with the marks obtained in the exam in POLI 308 (Y). POLI 344 (X)8 8 9 10 10 11 12 13 13 11 14 POLI 443 (Y) 7 11 8 7 12 11 10 12 14 17 15 (i) State the two equation lines of the regression line. (ii) If a student was absent from POLI 443 but scored 18 in POLI 344 (X) state the regression line, which would be suitable for estimating his/her possible mark in POLI 443 and work out a fair estimate for his /her possible mark.A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2for a sample of N=20N=20 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.02. X1X1 X2X2 YY 31.4 32.3 25.2 85.4 28.1 53 66.3 42.6 67.4 59 56.1 70.7 52.4 40.4 39.7 86.4 23.7 35 50.9 36.7 34.4 74.4 38 64.9 57.3 47.6 67.4 61.9 33.3 41.3 48.6 49.7 53.6 46.6 47.2 34.5 31.8 38.7 40.9 86 55 74 69.8 27.7 45.9 65.8 48.2 42.4 44.7 55.3 55.1 57.3 27 31.5 60.4 28.1 19.4 65.9 26 13.7 SSreg= SSres= R2= F= P-value = What is your decision for the hypothesis test? Reject the null hypothesis, H0:β1=β2=0 Fail to reject H0H0 What is your final conclusion? The evidence supports the claim that one or more of the regression coefficients is non-zero The evidence supports the claim that all of the regression…Consider the following table of N=3 observations. Calculate estimates of b1 and b0 (b-hat) considering the linear regression model y=b+b*x Compute SSE for this regression Assume that SST=32. What is R^2 for this regression?
- Consider the following population linear regression model of individual food expenditure: Y = 50 + 0.5X + u, where Y is weekly food expenditure in dollars, X is the individual’s age, and 50+0.5X is the population regression line. Suppose we generate artificial data for 3 individuals using this model. This artificial sample, which consists of 3 observations, is shown in the following table: Answer the following questions. Show your working. (a) What are the values of V1 and V4? (b) Suppose we know that in this artificial sample, the sample covariance between X and Y is 150, and the sample variance of X is 100. Compute the OLS regression line of the regression of Y on X. (Hint: Assume these summary statistics and the OLS regression line continue to hold in parts (c)-(e).) (c) What are the values of V5 and V7?Given a generic data set (x,y) with a linear regression. How do you determine if the y(dependent) will be less/greater than a certain value at a decided value of x?A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=20N=20 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.05α=0.05. X1X1 X2X2 YY 65.4 65.8 57.3 72.8 70.8 55.1 63.3 59.9 66.9 59.1 60.4 60.4 65.4 66.9 56.2 58.3 61.9 50.4 57.1 57.1 54.2 78.2 62.5 67.5 54.2 55.9 57.1 56.5 55.5 57.8 57.9 56.2 60.8 54.3 54.8 61.8 68.2 70.5 71.8 60 64.1 58.8 66.6 60.5 54.6 66.7 68.5 51.7 45.1 48.6 57.1 58.4 59.9 55.9 58.6 66.3 52.5 56 60.5 67.1 SSreg=SSres=R2=F=P-value =